Topology, Geometry, Integrable Systems, and Mathematical Physics: Novikov’s Seminar 2012–2014

Advances in the Mathematical Sciences

Volume: 234; 2014; 392 pp

MSC: Primary 00; 51; 53; 14; 55; 70; 76; 81; 39; 17

Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012–2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Graduate students and research mathematicians interested in applications of geometry and topology to mathematical physics.

• Chapters

• Andrei V. Alexeevski and Sergey M. Natanzon — Algebras of conjugacy classes of partial elements

• Iulia Beloshapka and Armen Sergeev — Harmonic spheres in the Hilbert–Schmidt Grassmannian

• Fedor Bogomolov and Christian Böhning — On uniformly rational varieties

• M. Boiti, F. Pempinelli and A. K. Pogrebkov — IST of KPII equation for perturbed multisoliton solutions

• Victor Buchstaber and Jelena Grbić — Hopf algebras and homology of loop suspension spaces

• Leonid O. Chekhov and Marta Mazzocco — Quantum ordering for quantum geodesic functions of orbifold Riemann surfaces

• Vladimir Dragović — Pencils of conics and biquadratics, and integrability

• B. Dubrovin — Gromov–Witten invariants and integrable hierarchies of topological type

• Ivan Dynnikov and Alexandra Skripchenko — On typical leaves of a measured foliated 2-complex of thin type

• Alexander A. Gaifullin — Volume of a simplex as a multivalued algebraic function of the areas of its two-faces

• G. M. Kemp and A. P. Veselov — Discrete analogues of Dirac’s magnetic monopole and binary polyhedral groups

• H. M. Khudaverdian and Th. Th. Voronov — Geometric constructions on the algebra of densities

• I. Krichever — Amoebas, Ronkin function, and Monge-Ampère measures of algebraic curves with marked points

• A. Ya. Maltsev — The averaging of multi-dimensional Poisson brackets for systems having pseudo-phases

• Andrey E. Mironov — Periodic and rapid decay rank two self-adjoint commuting differential operators

• O. I. Mokhov — Commuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients

• Maxim V. Pavlov and Sergey P. Tsarev — Classical mechanical systems with one-and-a-half degrees of freedom and Vlasov kinetic equation

• Oleg K. Sheinman — Lax operator algebras of type $G_2$

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